Fractions

Equivalent fractions

Look at the circle.

It is divided into 2 equal parts.

 \(1\over 2\)of the circle is coloured.

Now look at this circle.

It is divided into 4 equal parts.

\(2 \over 4\)of the circle is coloured.

You can see that the area coloured in both circles is same.

This means \(1\over 2\) and \(2 \over 4\)are equal

We call such fractions equivalent fractions.

Equivalent fractions are fractions which have different numerators and denomina[1]tors but have same value

Look again at these fractions.

\(1 \over 2\)     \(2 \over 4\)

You can see that to go from \(1 \over 2\) to \(2 \over 4\), we just doubled the numerator and the denominator

If you multiply \(1 \over 2\) by \(2 \over 2\) , you get  \(2\over 4\), which is equivalent to \(1 \over 2\).

When you divide your circle in twice number of parts, you have to take twice number of parts out to get the same fraction.

This means we can multiply numerator and denominator of a fraction with same number and we will get an equivalent fraction

Example 1: Let’s multiply \(2 \over 4\) by \({2\over 2}\)

You can see that \(2\over 4\) and \(4 \over 8\) also represent same fraction.

\(\frac{1}{2} = \frac{2}{4} = \frac{4}{8}\)

Example 2: Find equivalent fraction of \(2 \over 5\)

Let ‘s multiply \(2\over 5\)  by \(3\over 3\)

You can see that  \(2\over 5\) and \(6\over 15\) represent equivalent fraction

Example 3: Let’s find equivalent fraction of  \(4\over 6\).

We know that we can multiply the numerator and the denominator of a fraction by the same number and get an equivalent fraction

Let’s multiply  \(4\over 6\) by \(2\over 2\).

Now, we have 12 parts and 8 out of them are coloured.

You can see that the coloured part in \(4 \over 6\)  and  \(8\over 12\)is the same

We can also divide the numerator and denominator of a fraction by the same number and get an equivalent fraction. Now, we have 3 parts and 2 of them are coloured

Now, we have 3 parts and 2 of them are coloured. You can see that the coloured part is the same

Look at this equivalent fraction pair. Can you find the missing number?

We know that to find equivalent fractions, we multiply or divide numerator and denom[1]inator of a fraction by the same number.

Recall your tables. To get 6 from 3, we will multiply 3 by 2.

 3 times 2 is 6

Which means we have to multiply numerator of the fraction by 2 as well

1 times 2 is 2

3 times 2 is 6.

 \(2\over 6\) is the required equivalent fraction